You have short rate models, https://en.wikipedia.org/wiki/Short-rate_model, but there doesnt seem to be any long rate models.

I find this weird as in options modelling you model the whole smile, not just a portion of it.

What I am missing?

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    $\begingroup$ In the early days (at the time of Vasicek, Cox) it was thought that the right short term i.r. model would also determine long rates via the Expectations Hypothesis. So there would be no need for anything else. But no short term model good enough to do this was developed, one that would generate realistic behavior at all maturities. (The yield curves generated by the popular models are pretty simplistic compared to the actual ones) And we don't quite know how to model things like liquidity and term premia. So the research is kind of stuck; if you have ideas let us know. $\endgroup$ – Alex C Aug 19 '18 at 17:09
  • $\begingroup$ @AlexC can you explain the mechanism from a model for stir via EH? I dont understand the logic. $\endgroup$ – Permian Aug 19 '18 at 17:15
  • $\begingroup$ @AlexC I dont see the complications with liquidity and term premia. Should this be a separate question? $\endgroup$ – Permian Aug 19 '18 at 17:16
  • $\begingroup$ I guess if you answers those it probably should be a formal answer $\endgroup$ – Permian Aug 19 '18 at 17:16
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    $\begingroup$ It’s only a choice of how sophisticated you want to be, and how much effort and computational power you want to invest in your model. This is driven by what application you’re looking at. If you’re looking to trade exotic rate products, then you’ll definitely go for a proper model like LMM or better, for other more mundane applications, simpler models are enough. $\endgroup$ – Ivan Aug 23 '18 at 17:33

It comes down to what is meant by long rate.

I will approach the problem as follow: Would a 5 year rate be called a long rate? How about 10 years rate then? How about 2 years rate? It won’t be easy to link all these rates, without some modelling of the rates between these tenors. And that’s exactly what the forward rates models do.

Hope this helps!

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